展开 (1-z^{-1})(1-z^{-1})^2

解答

展开

(1 - z^{- 1}) (1 - z^{- 1})^{2}

- \frac{3}{z} + \frac{3}{z ^{2}} - \frac{1}{z ^{3}} + 1

求解步骤

(1 - z^{- 1}) (1 - z^{- 1})^{2}

使用分配律:

a (b - c) = ab - a c

a = (1 - z^{- 1})^{2}, b = 1, c = z^{- 1}

= (1 - z^{- 1})^{2} \cdot 1 - (1 - z^{- 1})^{2} z^{- 1}

= 1 \cdot (1 - z^{- 1})^{2} - z^{- 1} (1 - z^{- 1})^{2}

化简

1 \cdot (1 - z^{- 1})^{2} - z^{- 1} (1 - z^{- 1})^{2} : - \frac{3}{z} + \frac{3}{z ^{2}} - \frac{1}{z ^{3}} + 1

= - \frac{3}{z} + \frac{3}{z ^{2}} - \frac{1}{z ^{3}} + 1

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